IAU Symposium 301
Precision Asteroseismology
Reaching the 1% accuracy level on stellar mass and
radius determinations from asteroseismology
The case of hot subdwarf B stars
Valerie Van Grootel
(University of Liege)
S. Charpinet (IRAP Toulouse), G. Fontaine (U. Montreal), P. Brassard (U.
Montreal), and E.M. Green (U. Arizona)
1.
Introduction to hot subdwarf B (sdB) stars
Hot (Teff  20 000 - 40 000 K) and compact (log g  5.2 - 6.2) stars
•
Core He-burning, extremely thin H-rich envelope
• sdBs are thought to be post-RGB stars having lost
most of their H-envelope through binary interaction
(stellar, sub-stellar and planet)
• p-mode and g-mode pulsators
Mass distribution of sdB stars
•
To date: 15 sdB pulsators modeled by seismology
•
•
•
Mass: ~1% precision
log g: ~0.1% precision
Radius: ~0.6% precision
Is this reliable? Is this accurate? Is this really so precise?
Valérie Van Grootel – IAU Symposium 301
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2. PG 1336-018, the Rosetta stone of sdB seismology
pulsating sdB+dM eclipsing binary (Porb=2.4244h)
Eclipses and light curve modeling (multicolor photometry ULTRACAM@VLT)
+accurate spectroscopy (RV curve UVES@VLT):
orbital solutions for mass, radius (and log g) of the sdB component
(Vuckovic et al. 2007, A&A, 471, 605)
•
Whole Earth Telescope campaign: 25 pulsation
periods for the sdB component in the range 96-205s
(p-modes), Kilkenny et al. 2003 (MNRAS, 345, 843)
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3.
The forward modeling approach for asteroseismology
The method consists of finding the best possible match between the observed
frequencies and those computed from models  optimization procedure
Stellar model
computation
Parameters (a1,a2,..,aN)
Pulsation
computation
Spectroscopy
(Teff, log g)
Computed
periods
Period matching
code (Genetic
Algorithm)
Observed
periods
Observations
Valérie Van Grootel – IAU Symposium 301
min. S2(a1,a2,..,aN)
the optimal model is the
seismic solution
Mode identification (if available)
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3.
The forward modeling approach for asteroseismology
Error estimates: using probability distributions (Van Grootel et al. 2013,A&A, 553, 97)
Likelihood function
Probability density function for parameter a1 (ex. mass):
(with
)
Questions:
•
•
•
Is the best-fit model the most representative model of the star?
Are seismic estimates accurate (do model uncertainties introduce
systematics on parameters determined from seismology)?
Are seismic estimates precise (error estimates reliable)?
Valérie Van Grootel – IAU Symposium 301
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4. Seismic analysis of the pulsating sdB PG 1336-018
•
•
Optimization procedure is launched in a vast parameter space where sdB stars are found
(details in Van Grootel et al. 2013, A&A, 553, 97)
Best-fit solution to the 25 observed periods:
Density of probability
3 orbital solutions (Vuckovic et al. 2007)
for the sdB mass
sdB mass from seismology:
0.471 ± 0.006 Ms
(1.3% precision)
•
•
1σ range
Valérie Van Grootel – IAU Symposium 301
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Consistent within 1σ the orbital
mass 0.466 ± 0.006 Ms
No significant difference, the
mass measurement is accurate
The best-fit mass (min. S2) is in
the 1σ range (not an outlier)
Optimal model (min S2)
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4. Seismic analysis of the pulsating sdB PG 1336-018
Surface gravity log g
•
•
•
Stellar radius
Seismic solution: 5.775 ± 0.007
(0.1% precision)
Orbital solution: 5.77 ± 0.06
Spectroscopy: 5.771 ± 0.015
•
•
1σ range
Seismic solution: 0.147 ± 0.001
Rs (0.6% precision)
Orbital solution: 0.15 ± 0.01 Rs
1σ range
Optimal model (min S2)
•
No significant difference, R and log g are accurately derived
• Best-fit (min S2) R and log g in the 1σ range
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5. Precision and accuracy of seismology
In summary:
Stellar models for asteroseismology of sdB stars allow for both precise and
accurate determinations of the stellar parameters, in particular mass and radius.
But how do the model uncertainties impact this result ?
3 main sources of uncertainties in sdB models:
•
Envelope Iron profile (standard: radiative levitation=gravitational settling)
•
Core/envelope transition profile (standard: not smoothed by diffusion)
•
He-burning nuclear reaction rates (standard: Caughlan & Fowler 1988)
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5. Precision and accuracy of seismology: envelope iron profile
Green: uniform solar profile
Black: standard profile (radiative levitation =
gravitational settling)
Red: standard/2
Blue: standard/4
We redo 3 seismic analyses of PG 1336-018 with the modified models. Results:
No drift on stellar mass
2σ drift on log g and radius
Despite significant changes in the iron abundance profiles, the derived
parameters are mostly unaffected (e.g. the mass) or only subject to very
small systematic drifts
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5. Precision and accuracy of seismology
Core/Envelope transition profile
sharp
smooth
He-burning rate: 12C(α,γ)16O x2
(Angulo et al. 1999)
No significant drift on stellar mass, radius and log g
The seismic solution is robust against uncertainties in
the constitutive physics of the models
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6. Conclusion
Conclusion:
•
Seismic parameters determined from asteroseismology for sdB stars
are both precise, accurate, and robust again model uncertainties
The best-fit (optimal) model is the most representative model of the star
•
We can indeed achieve ~1% accuracy for mass and radius
determinations from asteroseismology
Remarks:
•
We are still (very) far from reproducing the precision of the observations (1
nHz for Kepler, 0.1μHz for ground-based; vs 10μHz for seismic model)
Asteroseismology has still not delivered its full potential
-
To provide extremely accurate global parameters (M, R, log g…)
To probe internal structure, composition and physics (effects of
diffusion…). Sensitivity of g-modes to the stellar interior.
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